4 citations · 5 across the 16 of their papers we have counts for
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Splitting schemes for problems with memory
Petr N. Vabishchevich
The paper considers the Cauchy problem for a first-order integro-differential equation with memory in a finite-dimensional Hilbert space. The main computational difficulty of such…
Operator-difference approximations on two-dimensional merged Voronoi-Delaunay grids
Petr N. Vabishchevich
Formulating boundary value problems for multidimensional partial derivative equations in terms of invariant operators of vector (tensor) analysis is convenient. Computational algor…
Decoupling technology for systems of evolutionary equations
Petr N. Vabishchevich
Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components…
Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations
Yalchin Efendiev, Wing Tat Leung, Wenyuan Li +2
In this paper, we consider a class of convection-diffusion equations with memory effects. These equations arise as a result of homogenization or upscaling of linear transport equat…
Approximate solution of the Cauchy problem for a first-order integrodifferential equation with solution derivative memory
Petr N. Vabishchevich
We consider the Cauchy problem for a first-order evolution equation with memory in a finite-dimensional Hilbert space when the integral term is related to the time derivative of th…
Numerical solution of the Cauchy problem for Volterra integrodifferential equations with difference kernels
Petr N. Vabishchevich
We consider the problems of the numerical solution of the Cauchy problem for an evolutionary equation with memory when the kernel of the integral term is a difference one. The comp…